Verified Solution • 2025–26 Session moderate

QJEEM21Ma3e35: JEE Main 2021 Mathematics - Class 11 JEEM21Ma3e35 Solution: Consider three observations a, b, and c such that b = a + c. If …

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

Multiple Choice Options

  • A b2 = 3(a2 + c2) + 9d2
  • B b2 = 3(a2 + c2) −- 9d2
  • C b2 = 3(a2 + c2 + d2)
  • D b2 = a2 + c2 + 3d2

Step-by-Step Verified Solution

For a, b, c

mean = x‾=a+b+c3\overline x = {{a + b + c} \over 3}

x‾=2b3\overline x = {{2b} \over 3}

We know, S.D. of a + 2, b + 2, c + 2 = S.D. of a, b, c = d

d2=a2+b2+c23−4b29{d^2} = {{{a^2} + {b^2} + {c^2}} \over 3} - {{4{b^2}} \over 9}

b2=3a2+3c2−9d2{b^2} = 3{a^2} + 3{c^2} - 9{d^2}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring